Question

Find the equation of the hyperbola satisfying the give conditions: Foci (0, ±13), the conjugate axis is of length 24.

Answer 1

Foci (0, ±13), the conjugate axis is of length 24.
Here, the foci are on the y-axis.
Therefore, the equation of the hyperbola is of the form $\frac{x^2}{a^2} – \frac{y^2}{b^2} = 1.$
Since the foci are (0, ±13), c = 13.
Since the length of the conjugate axis is 24, 2b = 24
$⇒$ b = 12.
We know that $a ^2 + b ^2 = c ^2 .$
∴ a2 + 122 = 132
$⇒$ a2 = 169 – 144
= 25

Thus, the equation of the hyperbola is $\frac{y^2}{25} – \frac{x^2}{144} = 1$